{"id":"bb9c275a-b5c5-41b5-9b5f-6c516b0fcde5","arxiv_id":"2412.13198","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"A directed grid of connected units, unfolded under Integrated Information Theory, specifies a cause-effect structure with properties that match the phenomenology of temporal flow, so experienced time is a structure, not a process.","lead":"This paper argues that the feeling of time flowing can be explained by the brain's causal structure rather than by a process unfolding in clock time. It uses Integrated Information Theory to show that a small network with directed connections produces a structure with the same abstract properties as our experience of moments moving from now to then.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim rests on a partial analysis: only contiguous distinctions and 2-relations are checked; the full cause–effect structure's flow properties are asserted, not demonstrated.","rationale":"The reader's CONDITIONAL verdict is appropriate, and my concern supports it without changing the verdict. The weakest assumption I identify is not the phenomenological classification but the completeness of the structural demonstration. This concern is more load-bearing because even granting the phenomenology and the IIT identity axiom, the conclusion would not follow unless the entire cause-effect structure, not a selected fragment, instantiates the flow properties. The paper's own hedges in §3.1.2 and §4.1 make the gap textual, not an external dispute. It is also directly testable with PyPhi, which the authors already use, so the condition is feasible. The reader's rationale did ask for analysis of the full cause-effect structure including higher-degree relations, so there is partial agreement, though the reader's stated weakest assumption was the introspective phenomenology and the directed-grid substrate conjecture, not this internal completeness gap. My concern thus sharpens the conditional: accept only after a full-structure verification shows that the entire cause-effect structure, not just contiguous 2-relation fragments, satisfies the four flow properties.","tokens_in":27244,"tokens_out":4257,"duration_ms":38869,"concrete_test":"Use PyPhi to unfold the complete cause–effect structure of the seven-unit directed grid in state abcDefG, without filtering by mechanism contiguity or relation degree. Enumerate all 79 irreducible distinctions and, for each, check whether cause and effect purviews are asymmetric/non-identical (directedness). For every pair and triple of distinctions, check whether the inclusion, connection, and fusion conditions of §4.3–4.5 are satisfied, including higher-degree relation faces. Report any violating distinction or relation. Then repeat the full enumeration on directed grids with 5, 9, and 11 units using the same weight pattern (w=0.3 self, 0.6/0.1 lateral) to test whether the flow property is a generic feature of the substrate class or an artifact of the particular 7-unit instance.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the claim that the whole cause–effect structure of a directed grid is a flow, not merely the exemplary fragments shown. Section 4.1 restricts attention to contiguous mechanisms ('nearly a third of the distinctions ... will be the focus for the account below'), and Section 3.1.2 explicitly limits the analysis to 2-relations and 2-faces. Figures 5–8 then demonstrate directedness, inclusion, connection, and fusion for a small set of overlapping contiguous distinctions (bcDef, cDef, bcDe, cDe). The Figure 8 caption asserts that 'This holds for the other distinctions that compose the cause–effect structure,' but no computation or proof is provided for the remaining irreducible distinctions (mostly non-contiguous mechanisms) or for higher-degree relations. This matters because the paper's own phenomenology allows moments to be non-contiguous ('two notes separated by a pause'), so those distinctions cannot be set aside. If any non-contiguous distinction or higher-degree relation violates one of the four defining properties, the cause–effect structure is not a flow, and the central identity claim—that experienced flow is explained by the full cause–effect structure—is unsupported. The paper's own scope limitations therefore leave a gap between the demonstrated examples and the universal explanatory claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an IIT 4.0 account of temporal experience. It argues that the conscious present is experienced as flowing because it is composed of directed phenomenal distinctions (moments) bound by directed inclusion, directed connection, and directed fusion. The authors then model a seven-unit directed 1D grid with an external input delay line, unfold its cause–effect structure using PyPhi, and show that several contiguous distinctions (bcDe, cDef, bcDef, cDe) and their 2-relations exhibit properties corresponding to the four phenomenal properties. They conclude that the experienced present does not correspond to a process in clock time but to a static cause–effect structure, so that time is a structure rather than a process.","tokens_in":27484,"tokens_out":8405,"duration_ms":71718,"significance":"If the full cause–effect structure of directed grids indeed satisfies the four flow properties, the paper extends IIT's explanatory identity from spatial extension to temporal flow, offering a principled and computationally explicit account of why time feels flowing. The use of PyPhi makes the worked computations reproducible, and Section 4.13 contains falsifiable predictions (e.g., present duration proportional to grid size, now/then terminus activation effects). However, the universal claim currently rests on a partial analysis of the cause–effect structure and on a strong phenomenological premise about the sufficiency of the four properties. The paper is transparent about several of its limitations, which is commendable, but the gap between the demonstrated examples and the global conclusion must be addressed before the central identity claim is fully supported.","major_comments":[{"comment":"The paper's central claim—that the cause–effect structure of a directed grid is a flow—is demonstrated only for a subset of distinctions and relation types. Section 3.1.2 explicitly limits the analysis to 2-relations and 2-faces, and Section 4.1 states that 'nearly a third of the distinctions are specified by contiguous units' and that these will be the focus. The Figure 8 caption then asserts, without computation or proof, that 'This holds for the other distinctions that compose the cause–effect structure.' Since the paper's own phenomenology (Section 2.1) includes moments such as 'two notes separated by a pause,' which are non-contiguous, and since higher-degree relations are part of the cause–effect structure, the universal identity claim is not supported by the presented evidence. This gap is load-bearing for the Abstract's conclusion that directed grids account for the feeling of time flowing.","section":"§3.1.2, §4.1, Figure 8 caption"},{"comment":"The computational demonstration is a single instance: a 7-unit directed grid with hand-chosen weights (self-weight 0.3, lateral weights 0.6 and 0.1) in the single state abcDefG. The paper does not show that directedness, directed inclusion, directed connection, and directed fusion hold for other weight configurations, other states, or other grid lengths, nor does it provide an analytic argument for arbitrary directed grids. Without such a generalization, the statement in §4.6 that 'the cause–effect structure unfolded from a directed grid is composed of distinctions that are directed...' is an overgeneralization from one example.","section":"§4.2–4.5, §3.2"},{"comment":"The sufficiency of the four phenomenal properties is asserted rather than established. Section 2 states that directedness, directed inclusion, directed connection, and directed fusion are 'necessary and sufficient for the experience of time,' but no independent operationalization or empirical criterion is given; 'flow' is then defined in §4.6 simply as a cause–effect structure satisfying those same properties. This makes the central correspondence partly circular. The paper also sets aside experienced speed in §2 ('the feeling of temporal flow only refers to... rather than to the experienced speed'), yet §4.13 later appeals to modulations of synaptic strength to account for slowing or speeding of time; the authors should clarify how these statements are compatible.","section":"§2, §4.6, §4.13"},{"comment":"The conjecture that arrays of directed grids in auditory and other posterior cortices are the substrate of temporal experience is acknowledged to have little direct evidence. This is a legitimate hypothesis, but it means the predictions in §4.13 are conditional on an unverified substrate. The paper should more sharply separate the formal cause–effect result—what directed grids would imply if they were the substrate—from the empirical conjecture about where such grids are located in the brain.","section":"§4.12"}],"minor_comments":[{"comment":"The sentence 'The input array not only provides bottom-up inputs...; is also works as a delay line' contains a typo: 'is also works' should be 'it also works.'","section":"§3.2"},{"comment":"The displayed equation for sigma(I*; s_k, w_k, I) is typeset with garbled subscripts and superscripts; it needs proper mathematical formatting for the equation to be readable.","section":"§3.2"},{"comment":"The text cites Arstila (2015) in §4.13 and Arstila (2018) in §4.15, but the reference list contains only Arstila (2023); please add the missing references or correct the in-text citations.","section":"References"},{"comment":"In the caption, 'coincides with the union the purviews of bcDef' is missing 'of': it should read 'coincides with the union of the purviews of bcDef.'","section":"Figure 8 caption"},{"comment":"The phrase 'Lateral and back-connections connections' contains a duplicated 'connections'; it should be 'Lateral and back-connections.'","section":"§4.12"},{"comment":"The PyPhi citation appears as 'W. G. P. Mayner et al., 2018' in the text but as 'Mayner, W., Marshall, W., ...' in the reference list; please standardize the citation style.","section":"§3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a theory paper within the IIT framework and would be of interest to the consciousness and IIT community. The main risk is the gap between the worked examples and the universal claim that the full cause–effect structure of a directed grid is a flow. This gap is potentially closable by either a formal argument for all distinctions and relation degrees or a carefully scoped claim that limits the explanatory identity to the demonstrated subset. I therefore recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know first: this is a theory-internal proof of concept, not an empirical test. The genuinely new result is that unfolding IIT 4.0 on a directed 1D grid yields causal distinctions and relations that mirror four phenomenal properties of temporal flow—directedness, directed inclusion, connection, and fusion. That extends Haun and Tononi's undirected-grid account of space to time in a non-obvious way. The PyPhi computation on a 7-unit grid is concrete and reproducible, and the authors are upfront that they only analyze contiguous mechanisms and 2-relations.\n\nWhat the paper does well: the phenomenology section is careful and distinguishes flow from experienced speed or a sense of passage. It engages seriously with Husserl and James on retention and protention, and it spells out the physical correspondence both locally and at the level of contexts. The authors are honest about scope: small substrate, conjectured neural substrate, no direct evidence for directed grids in auditory cortex. They also make falsifiable predictions, such as the proportionality between grid size and the duration of the extended present.\n\nThe soft spots are real but not fatal to the proof-of-concept. The main one: the central claim that the whole cause–effect structure is a flow is asserted rather than demonstrated. Section 4.1 restricts to contiguous distinctions, Section 3.1.2 limits analysis to 2-relations, and the Figure 8 caption simply says \"this holds for the other distinctions\" without proof. Since the paper's own phenomenology includes non-contiguous moments (two notes separated by a pause), those cannot be set aside. If a non-contiguous distinction or a higher-degree relation violates one of the four properties, the structure is not a flow. That gap is load-bearing for the universal explanatory claim. Second, the four phenomenal properties are asserted as necessary and sufficient from introspection, with no independent operationalization. Third, the identity claim depends on IIT's unexplained axiom—fine for IIT partisans, but it limits the paper's reach.\n\nWho is this for? Consciousness researchers, philosophers of time, and the IIT community. As a proof of concept within IIT, it deserves a serious referee. The missing analysis is fixable: compute the full cause–effect structure for the 7-unit grid and larger grids, check all distinctions and higher-order relations, and do sensitivity analysis on the hand-chosen weights. Recommendation: send it out, but require either the full computation or a softened claim.","headline":"IIT's directed-grid story for temporal flow is a genuine extension of the spatial account, but the universal claim outruns the demonstrated examples.","tokens_in":28055,"tokens_out":2193,"would_cite":true,"duration_ms":22522,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that the feeling of time flowing is explained by the cause-effect structure of directed grids in the brain, making time a structure rather than a process.","keywords":["temporal experience","integrated information theory","cause-effect structure","directed grid","specious present","temporal flow","consciousness","IIT 4.0"],"falsifier":"A psychophysical test could settle the sufficiency claim: if subjects can report differences in the experienced speed or felt passage of time while the four structural properties are held constant, then the four properties are not sufficient and the directed-grid flow would not explain the feeling of temporal flow.","tokens_in":1712,"feed_emoji":"⏳","tokens_out":1596,"duration_ms":64828,"temperature":0.7,"pith_summary":"This paper tries to give an objective account of why time feels flowing, not by appealing to clocks or to a process unfolding in the brain, but by showing that a specific causal structure can reproduce the felt order of moments. It claims that four introspectible properties of temporal experience—directedness, directed inclusion, directed connection, and directed fusion—are necessary and sufficient for the feeling of flow, and that these correspond exactly to properties of the cause-effect structure unfolded from a directed 1D grid under Integrated Information Theory 4.0. If correct, the conscious present is a single static cause-effect structure specified by the brain's current state, so time is a structure rather than a process. A sympathetic reader would care because this would extend a principled physical account of the quality of experience from space to time, with testable predictions about the duration and grain of the present.","feed_headline":"Time feels flowing because the brain builds a directed causal structure","feed_subtitle":"A seven-unit directed grid's cause-effect structure reproduces the felt succession of moments, the paper argues.","key_machinery":"The load-bearing object is the directed 1D grid: seven binary units with asymmetric nearest-neighbor connections (self-connection weight 0.3, stronger lateral weight 0.6, weaker lateral weight 0.1), driven by an input array that acts as a delay line preserving a trace of roughly 210 milliseconds of clock time. Under the IIT 4.0 formalism, the grid's current macro state (about 30 milliseconds) unfolds into a cause-effect structure of causal distinctions—mechanisms with cause and effect purviews—and causal relations formed by congruent overlaps among purviews. The asymmetry between cause and effect purviews gives directedness, and the systematic overlaps among distinctions realize directed inclusion, connection, and fusion; a cause-effect structure satisfying all of these is called a flow.","core_discovery":"The paper's central claim is that a directed 1D grid of seven probabilistic units, in its current macro state, unfolds under IIT 4.0 into a cause-effect structure in which causal distinctions are directed—causes lean toward the now and effects toward the then—and are bound by relations of directed inclusion, connection, and fusion. These structural properties match, one by one, the phenomenal properties that the paper argues make up the experience of temporal flow: moments point away from themselves, nest within one another, overlap in an ordered way, and compose larger moments. The experienced present is therefore not a process unrolling in clock time; it is a cause-effect structure specified by a system in its current state. Time, on this account, is a structure, not a process.","pith_inferences":["If the four properties are truly sufficient, then any physical system whose unfolded cause-effect structure is a flow—not just neural grids—would have temporal experience; this is an implication the paper does not develop.","The account suggests that experienced duration, boundary, and interval are derived from inclusion and connection relations rather than read off clock time, which could give a structural explanation of time illusions such as the oddball effect or temporal ventriloquism.","The claim that time is a structure rather than a process, if extended, would align with block-universe views: passage would be an intrinsic property of a state rather than motion along a temporal axis, which would reframe, not resolve, the metaphysics of time.","One testable extension is that if the now terminus is preferentially connected to action-related areas, then perturbing those connections should shift the felt now relative to action without changing the felt order of moments."],"forward_implications":["If the account is right, the felt present is not a replay of neural activity over hundreds of milliseconds; it is a single macro state lasting about 30 milliseconds that encodes a roughly 210-millisecond trace through its cause-effect structure.","The duration of the experienced present should scale with the number of units in a directed grid, so larger grids would support longer presents and higher-level areas could bind longer sequences of events.","Artificial activation near the now terminus of a directed grid should make a stimulus feel present, while activation near the then terminus should make it feel as if it occurred earlier.","Postdictive effects, protention, and the felt salience of the now are accommodated by top-down influences and by denser connectivity at the now end of the grid.","Temporal and spatial experience share the same explanatory scheme: directed 1D grids yield flow, while non-directed 2D or 3D grids yield spatial extension."],"supporting_citations":[{"why":"It supplies the IIT 4.0 formalism and postulates used to unfold cause-effect structures.","marker":"Albantakis et al. (2023)"},{"why":"It establishes the spatial account on which this paper builds and introduces the subtext and supertext context machinery.","marker":"Haun & Tononi (2019)"},{"why":"It provides the notion of the specious present and the distinction between a succession of experiences and experienced succession.","marker":"James (1890)"},{"why":"It frames retention and protention, which the paper uses to locate flow from the now to the then.","marker":"Husserl (1991)"},{"why":"It provides PyPhi, the software used to compute the unfoldings reported in this paper.","marker":"W. G. P. Mayner et al. (2018)"},{"why":"It documents the complete IIT 4.0 formalism referenced for distinctions, relations, and computations.","marker":"Integrated Information Theory Wiki (2024)"},{"why":"It supplies the activation functions and short-term plasticity mechanism that make the grid endorse its driven state.","marker":"W. Mayner et al. (2024)"}],"fun_headline_variants":["Time as structure, not process: a causal account of felt flow","Directed neural grids may explain why time feels like it flows","Why time feels flowing: it's a causal structure, not a process","Felt time emerges from directed cause-effect structures, IIT argues"],"cache_read_input_tokens":30080,"weakest_assumption_plain":"The argument rests on the introspective claim that the feeling of temporal flow is fully captured by four properties—directedness, directed inclusion, directed connection, and directed fusion—so if flow has an essential ingredient beyond these, such as experienced speed or a separate sense of passage, the directed-grid account would not explain it.","fun_headline_variants_meta":{"raw":{"variants":["Time as structure, not process: a causal account of felt flow","Directed neural grids may explain why time feels like it flows","Why time feels flowing: it's a causal structure, not a process","Felt time emerges from directed cause-effect structures, IIT argues"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000171,"raw_usage":{"total_tokens":1308,"prompt_tokens":1017,"completion_tokens":291,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":633,"completion_tokens_details":{"reasoning_tokens":217}},"tokens_in":633,"tokens_out":291,"duration_ms":3409,"temperature":1.0,"reasoning_tokens":217,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:31:18.924734+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A psychophysical test could settle the sufficiency claim: if subjects can report differences in the experienced speed or felt passage of time while the four structural properties are held constant, then the four properties are not sufficient and the directed-grid flow would not explain the feeling of temporal flow.","supporting_citations":[],"review_version":1}